arXiv subjects

Marco Zoli

Publications and source records attributed to Marco Zoli.

At least 19 recordsLinked to original sources

arXiv2025

Statistical method for A-RNA and B-DNA

Nucleic acids have been regarded as stiff polymers with long-range flexibility and generally modeled using elastic rod models of polymer physics. Notwithstanding, investigations carried out over the past few years on single fragments of order $\sim 100$ base pairs have revealed remarkable flexibility properties at short scales and called for theoretical approaches that emphasize the role of the bending fluctuations at single sites along the molecule stack. Here, we review a three dimensional mesoscopic Hamiltonian model which assumes a discrete representation of the double stranded (ds) molecules at the level of the nucleotides. The model captures the fundamental local interactions between adjacent sugar-phosphate groups and the pairwise interactions between complementary base pair mates. A statistical method based on the path integral formalism sets the ensemble of the base pair breathing fluctuations which are included in the partition function and permits to derive the thermodynamics and the elastic response of single molecules to external forces. We apply the model to the computation of the twist-stretch relations for fragments of ds-DNA and ds-RNA, showing that the obtained opposite pattern (DNA overtwists whereas RNA untwists versus force) follows from the different structural features of the two helices. Moreover, we focus on the DNA stretching due to the confinement in nano-pores and, finally, on the computation of the cyclization probability of open ends molecules of $\sim 100$ base pairs under physiological conditions. The mesoscopic model shows a distinct advantage over the elastic rod model in estimating the molecule bendability at short length scale.

cond-mat.soft↗

arXiv2023

Statistical models for nucleic acids

ds-RNA and standard ds-DNA show specific structural differences in their di-nucleotide steps, piled along the helical axis. Modeling the helices of short fragments by a 3D mesoscopic Hamiltonian model, I use path integral techniques to compute the average helical repeat and show that these structural features are at the origin of the opposite twist-stretch patterns of the A- and B- form.

cond-mat.soft↗

arXiv2023

Twist-stretch relations in nucleic acids

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules.

cond-mat.soft↗

arXiv2022

Mesoscopic helical models for DNA

Nucleic acids physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse grained models, e.g. the worm-like-chain, taken from polymer physics. In this article, I present an intermediate (mesoscopic) approach and show how to build a three dimensional Hamiltonian model which accounts for the main interactions responsible for the stability of the helical molecules. While the 3D mesoscopic model yields a sufficiently detailed description of the helix at the level of the base pair, it also allows one to predict the thermodynamical and structural properties of molecules in solution. Relying on the idea that the base pair fluctuations can be conceived as trajectories, I have built a computational method based on the time dependent path integral formalism to derive the partition function. While the main features of the method are presented, I focus here in particular on a newly developed statistical method to set the maximum amplitude of the base pair fluctuations, a key parameter of the theory. Some applications to the calculation of DNA flexibility properties are discussed together with the available experimental data.

cond-mat.soft↗

arXiv2022

Context-Aware Security for 6G Wireless The Role of Physical Layer Security

Sixth generation systems are expected to face new security challenges, while opening up new frontiers towards context awareness in the wireless edge. The workhorse behind this projected technological leap will be a whole new set of sensing capabilities predicted for 6G devices, in addition to the ability to achieve high precision localization. The combination of these enhanced traits can give rise to a new breed of context-aware security protocols, following the quality of security (QoSec) paradigm. In this framework, physical layer security solutions emerge as competitive candidates for low complexity, low-delay and low-footprint, adaptive, flexible and context aware security schemes, leveraging the physical layer of the communications in genuinely cross-layer protocols, for the first time.

cs.CR↗

arXiv2021

Base pair fluctuations in helical models for nucleic acids

A statistical method is developed to estimate the maximum amplitude of the base pair fluctuations in a three dimensional mesoscopic model for nucleic acids. The base pair thermal vibrations around the helix diameter are viewed as a Brownian motion for a particle embedded in a stable helical structure. The probability to return to the initial position is computed, as a function of time, by integrating over the particle paths consistent with the physical properties of the model potential. The zero time condition for the first-passage probability defines the constraint to select the integral cutoff for various macroscopic helical conformations, obtained by tuning the twist, the bending and the slide motion between adjacent base pairs along the molecule stack. Applying the method to a short homogeneous chain at room temperature, we obtain meaningful estimates for the maximum fluctuations in the twist conformation with $\sim 10.5$ base pairs per helix turn, typical of double stranded DNA helices. Untwisting the double helix, the base pair fluctuations broaden and the integral cutoff grows. The cutoff is found to increase also in the presence of a sliding motion which shortens the helix contour length, a situation peculiar of dsRNA molecules.

cond-mat.soft↗

arXiv2020

First-passage probability: a test for DNA Hamiltonian parameters

A method is proposed to select the suitable sets of potential parameters for a one-dimensional mesoscopic Hamiltonian model, first introduced to describe the DNA melting transition and later extended to investigate thermodynamic and dynamical properties of nucleic acids. The DNA base pair fluctuations are considered as time dependent trajectories whose initial condition sets the no crossing constraint enforced in the path integral for the first-passage probability. Performing the path integration at room temperature, relations are established between the cutoff on the amplitude of the base pair fluctuations and the model parameters. In particular, it is shown that the non-linear stacking parameter should be $\sim 1$. The formalism here developed may be applied to compute the lifetime of open base pairs in three-dimensional helical models for DNA molecules.

cond-mat.soft↗

arXiv2020

Stretching DNA in hard-wall potential channels

A three dimensional mesoscopic model is applied to study the properties of short DNA chains in a confining environment. The cylindrical channel is represented by a hard-wall repulsive potential incorporated in the system Hamiltonian. The macroscopic helical parameters are computed performing statistical averages over the ensemble of microscopic base pair fluctuations. The average molecule elongation, measured by the end-to-end distance, is derived as a function of the channel potential parameters both for a homogeneous and a heterogeneous chain. The overall results suggest that the mesoscopic model, with the channel potential term, yields consistent quantitative estimates for the stretching and twisting of short chains.

cond-mat.soft↗

arXiv2019

Mesoscopic model for nano-channel confined DNA

I present a Hamiltonian model and a computational method suitable to evaluate structural and thermodynamic properties of helical molecules embedded in crowded environments which may confine the space available to the base pair fluctuations. It is shown that, for the specific case of a short DNA fragment in a nanochannel, the molecule is markedly over-twisted and stretched by narrowing the width of the channel.

cond-mat.soft↗

arXiv2019

DNA size in confined environments

For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders. The ds-DNA is modeled by a mesoscopic Hamiltonian which accounts for the three dimensional helical structure and incorporates fluctuational effects at the level of the base pair. The computational method assumes that the base pair fluctuations are temperature dependent trajectories whose amplitudes can be spatially modulated according to the crowders distribution. We show that the molecule elongation, as measured by the end-to-end distance varies non-monotonically with the strength of the confinement. Furthermore it is found that, if the crowders mostly confine the DNA mid-chain, the helix over-twists and its end-to-end distance grows in the strong confinement regime. Instead, if the crowders mostly pin one chain end, the helix untwists while the molecule stretches for large confinement strengths. Thus, our results put forward a peculiar relation between stretching and twisting which significantly depends on the crowders profile. The method could be applied to disegn specific DNA shapes by controlling the environment which constrains the molecule.

cond-mat.soft↗

arXiv2018

Short DNA persistence length in a mesoscopic helical model

The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available to base pair fluctuations and derive the partition function. The apparent persistence lengths of a set of short chains have been computed as a function of the twist conformation both in the over-twisted and the untwisted regimes, whereby the equilibrium twist is selected by free energy minimization. The obtained values are significantly lower than those generally attributed to kilo-base long DNA. This points to an intrinsic helix flexibility at short length scales, arising from large fluctuational effects and local bending, in line with recent experimental indications. The interplay between helical untwisting and persistence length has been discussed for a heterogeneous fragment by weighing the effects of the sequence specificities through the non-linear stacking potential.

cond-mat.soft↗

arXiv2018

End-to-end distance and contour length distribution functions of DNA helices

We present a computational method to evaluate the end-to-end and the contour length distribution functions of short DNA molecules described by a mesoscopic Hamiltonian. The method generates a large statistical ensemble of possible configurations for each dimer in the sequence, selects the global equilibrium twist conformation for the molecule and determines the average base pair distances along the molecule backbone. Integrating over the base pair radial and angular fluctuations, we derive the room temperature distribution functions as a function of the sequence length. The obtained values for the most probable end-to-end distance and contour length distance, providing a measure of the global molecule size, are used to examine the DNA flexibility at short length scales. It is found that, also in molecules with less than $\sim 60$ base pairs, coiled configurations maintain a large statistical weight and, consistently, the persistence lengths may be much smaller than in kilo-base DNA.

cond-mat.soft↗

arXiv2017

Twisting short dsDNA with applied tension

The twisting deformation of mechanically stretched DNA molecules is studied by a coarse grained Hamiltonian model incorporating the fundamental interactions that stabilize the double helix and accounting for the radial and angular base pair fluctuations. The latter are all the more important at short length scales in which DNA fragments maintain an intrinsic flexibility. The presented computational method simulates a broad ensemble of possible molecule conformations characterized by a specific average twist and determines the energetically most convenient helical twist by free energy minimization. As this is done for any external load, the method yields the characteristic twist-stretch profile of the molecule and also computes the changes in the macroscopic helix parameters i.e. average diameter and rise distance. It is predicted that short molecules under stretching should first over-twist and then untwist by increasing the external load. Moreover, applying a constant load and simulating a torsional strain which over-twists the helix, it is found that the average helix diameter shrinks while the molecule elongates, in agreement with the experimental trend observed in kilo-base long sequences. The quantitative relation between percent relative elongation and superhelical density at fixed load is derived. The proposed theoretical model and computational method offer a general approach to characterize specific DNA fragments and predict their macroscopic elastic response as a function of the effective potential parameters of the mesoscopic Hamiltonian.

cond-mat.soft↗

arXiv2017

Twist-stretch profiles of DNA chains

Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule's free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules.

cond-mat.soft↗

arXiv2016

Flexibility of short DNA helices under mechanical stretching

The flexibility of short DNA fragments is studied by a Hamiltonian model which treats the inter-strand and intra-strand forces at the level of the base pair. The elastic response of a set of homogeneous helices to externally applied forces is obtained by computing the average bending angles between adjacent base pairs along the molecule axis. The ensemble averages are performed over a room temperature equilibrium distribution of base pair separations and bending fluctuations. The analysis of the end-to-end distances and persistence lengths shows that even short sequences with less than $100$ base pairs maintain a significant bendability ascribed to thermal fluctuational effects and kinks with large bending angles. The discrepancies between the outcomes of the discrete model and those of the worm-like-chain model are examined pointing out the inadequacy of the latter on short length scales.

q-bio.BM↗

arXiv2016

J-factors of short DNA molecules

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain ends boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length ( N ) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.

cond-mat.soft↗

arXiv2015

Unwinding of circular helicoidal molecules versus size

The thermodynamical stability of a set of circular double helical molecules is analyzed by path integral techniques. The minicircles differ only in \textit{i)} the radius and \textit{ii)} the number of base pairs ($N$) arranged along the molecule axis. Instead, the rise distance is kept constant. For any molecule size, the computational method simulates a broad ensemble of possible helicoidal configurations while the partition function is a sum over the path trajectories describing the base pair fluctuational states. The stablest helical repeat of every minicircle is determined by free energy minimization. We find that, for molecules with $N$ larger than $100$, the helical repeat grows linearly with the size and the twist number is constant. On the other hand, by reducing the size below $100$ base pairs, the double helices sharply unwind and the twist number drops to one for $N=\,20$. This is predicted as the minimum size for the existence of helicoidal molecules in the closed form. The helix unwinding appears as a strategy to release the bending stress associated to the circularization of the molecules.

cond-mat.soft↗

arXiv2015

Helical Disruptions in Small Loops of DNA

The thermodynamical stability of DNA minicircles is investigated by means of path integral techniques. Hydrogen bonds between base pairs on complementary strands can be broken by thermal fluctuations and temporary fluctuational openings along the double helix are essential to biological functions such as transcription and replication of the genetic information. Helix unwinding and bubble formation patterns are computed in circular sequences with variable radius in order to analyze the interplay between molecule size and appearance of helical disruptions. The latter are found in minicircles with $< 100$ base pairs and appear as a strategy to soften the stress due to the bending and torsion of the helix.

cond-mat.soft↗